Wednesday, November 12, 2008

Constructivism and lack of practice

Here are two of the clues to America's current mathematics problem:

1."Student-centered" learning (or "constructivism")

2.Insufficient practice of basic skills

In an October email, Spokane's secondary mathematics coordinator reaffirmed this district's commitment to a "student-centered" approach to teaching (also sometimes called "discovery learning" or "constructivism"). In this approach, students often work as partners or in groups, and teachers act as "facilitators" rather than as "instructors." Students are encouraged to come up with their own multiple solutions to problems and to ask fellow students for help before asking the teacher.

Reform math curricula are typically built around a constructivist approach, probably because the 1989 Standards document from the National Council of Teachers of Mathematics calls for it (Stiff, 2001c; "Curriculum," 2004). Proponents say the approach leads to "deeper understanding," helpful collaboration and better student enjoyment of the process. Others say a dependence on it can hinder the learning process and frustrate students.

A local parent told me this story about when his daughter took a math class that used reform math curriculum Connected Mathematics: Students were told that "Juan" was mowing a lawn in a right-angle triangle. He wanted to figure out the length of the diagonal. The term "Pythagorean Theorem" (a2 + b2 = c2) wasn't presented. The students were to work in groups and figure out a way to get the answer. Finally, one student who knew the theorem provided it to her group. (Her group was the only one to get the right answer.) Incredibly, the teacher "chastised" the student for using the formula.

"A lot of parents don't believe it at first," the parent said to me. "Like, their kids are younger, they don't know, and they feel that parents are exaggerating, but it is the honest-to-God truth, and these stories get worse."

In small doses, constructivism can provide flavor to classrooms, but some math professors have told me the approach seems to work better in subjects other than math. That sounds reasonable. The learning of mathematics depends on a logical progression of basic skills. Sixth-graders are not Pythagorus, nor are they math teachers.

Meanwhile, anti-reform advocacy group Mathematically Correct provides an amusing take on constructivism ("What Is," 1996): "This notion holds that students will learn math better if they are left to discover the rules and methods of mathematics for themselves, rather than being taught by teachers or textbooks. This is not unlike the Socratic method, minus Socrates."

Insufficient Practice of Basic Skills

Another problem in math classrooms is the lack of practice. Instead of insisting that students practice math skills until they're second nature, educators have labeled this practice "drill and kill" and thrown it under a bus. I wish I had a dollar for every time I heard that phrase. It's a strange, flippant way to dismiss a logical process for learning. Drilling is how anyone learns a skill. Removing drilling from the learning process is like saying, "We'll just remove this gravity. Now stay put." Everyone drills - athletes, pianists, soldiers, plumbers and doctors. Drilling is necessary. It isn't good or bad - it's simply what must be done.

Imagine if I told chess players they had to figure out the rules of chess on their own, in fits and starts, by trial and error and by asking their fellow players. Imagine if I expected them to win games when they hadn't had a chance to practice.

In American education, the "worm" is not yet turning, but it might be looking over its shoulder. In its March 2008 report, the National Mathematics Advisory Panel reintroduced the notion of practicing the basics: "Practice allows students to achieve automaticity of basic skills - the fast, accurate, and effortless processing of content information - which frees up working memory for more complex aspects of problem solving" ("Foundations," 2008, p. 30).

But children in the system now are stuck with a process that asks them to work in diverse groups to reinvent thousands of years of math procedures that they then don't get to practice.

Some people enjoy puzzles on logic and process, where things might not be what they seem and where they've got to figure out subtle differences and new ways of thinking. But this esoteric, conceptual approach to math, with a constant struggle to understand the process, doesn't seem like a logical approach for children. Children are concrete thinkers who tend to appreciate concrete ideas. Children want instructions, direction and things that make sense. Many don't appreciate the daily grind of writing about math, of having to figure out what they're doing, of having to count on classmates for guidance, of trying to remember things they've done just once or twice and several weeks ago.

It's ironic that proponents of reform math criticize traditionalists for supposedly not knowing "how to teach math to children." The reform method seems completely oppositional to how children learn best.

I asked a Spokane student if she prefers the Connected Mathematics she gets in school over the Singapore Math she gets at home. She said, "In a way, Connected Mathematics is easier because you don't have to know as much math, but in a way, it's harder because you have to know more. You have to know exactly what they want."

She gave me an example of the classroom approach: Students are to gather in groups to discuss a problem. The problem might be a complicated twist on simplistic math, or it might be a concept they've never seen before. As the groups muddle around, they don't always agree on what's required. Sometimes, they don't have the necessary underlying skills. Some students become frustrated or bored. Trying to help each other, some confuse the others. They might come up with the right answer, or they might not, but - without practicing the new concepts - the class moves on to something new. Singapore Math, on the other hand, "might be harder as far as the math goes," she said, "but at least you know what they want."

I told her I thought her answer was articulate and enlightening. "I've spoken to a lot of people now," I said, "and you explained things very well." "That's because they teach it," she replied, "but I'm the one who has to learn it."

British head teacher suspends a quarter of her pupils in a year... and exam results soar

A head teacher has transformed academic achievement at her school by adopting a zero tolerance approach to bad behaviour. Caroline Haynes, 49, has handed out 478 exclusions at Tendring Technology College over the past year - an astonishing one in 20 of all those issued across the county. The crackdown has seen the number of pupils getting A* to C grades at GCSE soar from 48 per cent in 2004, when she joined the school, to 74 per cent this year.

Mrs Haynes attacked political pressure on schools to reduce exclusions in order to improve their Ofsted behaviour ratings. 'Statistics paint a false picture,' she said. 'Because we refuse to buckle under the pressure we had to work very hard to convince Ofsted inspectors that pupil behaviour is good, despite the figures. 'I could reduce exclusion rates tomorrow by not suspending pupils, but it would have a detrimental effect on the quality of teaching and unruly behaviour.'

Academic results at the college in Clacton-on-Sea, Essex, were rated as being below average in a 2003 Ofsted report. Mrs Haynes joined the following year and now issues more than two suspensions each day on average to the 1,880 pupils. The total of 478 over the year is the equivalent of one in four of the school's pupils. However, a recent report found the school to be 'good' or better in every category.

Under her regime, there is an escalating level of sanctions, including extra work, detentions and being placed 'on report'. One-day exclusions are dished out for offences such as failing to attend two after-school detentions. Longer exclusions are given for offences such as bullying, stealing, disruption, abuse of staff or fellow students, vandalism and racism. During exclusions pupils are set work and cannot return to classes until it is completed. They and their parents must also meet the head to discuss how to improve their behaviour.

Mrs Haynes said it was important pupils knew when they had 'crossed the line'. She added: 'Our pupils learn to deal with the consequences of their actions and our teachers are allowed to concentrate on their job rather than battle bad behaviour. Exam results have soared. I'm very proud.'

The school permanently excludes pupils for possessing an illegal substance or offensive weapon. Two were expelled last year. The Department for Children, Schools and Families said it trusted heads' judgment 'to decide what sanctions will work best'.

1 comment:

Robert
said...

Re: Constructivism and Lack of Practice, I came across this article from a link in my employer's Friday news bulletin. I'm reproducing it in full, since I'm not sure my employer would want links to its intranet site. Article below:----------Why does informal learning work?It has been proved by the Institute for Research on Learning that 80% of how people learn their jobs is through informal learning – watching others, trial and error, asking colleagues, calling the help desk - as opposed to formal training.

Informal learning can be defined as non-organised, non-systematic learning that can take place anywhere outside of the classroom. It occurs spontaneously and is usually the reaction to a practical situational problem.

A recent study of time-to-performance completed by Sally Anne Moore at Digital Equipment Corporation shows that formal learning typically provides 25% job effectiveness but it is informal learning that completes the journey to peak performance.

Informal learning is effective because it is personal - the individual decides what to learn and how to learn it. This decision is often the result of a specific need that the learner feels needs to be sorted out immediately. (end)----------That last paragraph echoes John Taylor Gatto's "An Underground History of American Education", where it talked about how people like George Washington, Benjamin Franklin, and Thomas Edison gained their educations - they knew how to read and write, add and subtract, and when they came across a specific need for certain knowledge, they would read a book on that knowledge, or go seek out, out of their own self-interest, a school that would teach the subject to them. And they would learn the subject they were interested in rather quickly.

Background

Primarily covering events in Australia, the U.K. and the USA -- where the follies are sadly similar.

The only qualification you really need for any job is: "Can you do it?"

Particularly in academe, Leftism is motivated by a feeling of superiority, a feeling that they know best. But how fragile that claim clearly is when they do so much to suppress expression of conservative ideas. Academic Leftists, despite their pretensions, cannot withstand open debate about ideas. In those circumstances, their pretenses are contemptible. I suspect that they are mostly aware of the vulnerability of their arguments but just NEED to feel superior

"The two most important questions in a society are: Who teaches our children? What are they teaching them?" - Plato

Keynes did get some things right. His comment on education seems positively prophetic: "Education is the inculcation of the incomprehensible into the indifferent by the incompetent.”

"If you are able to compose sentences in Latin you will never write a dud sentence in English." -- Boris Johnson

"Common core" and its Australian equivalent was a good idea that was hijacked by the Left in an effort to make it "Leftist core". That made it "Rejected core"

TERMINOLOGY: The English "A Level" exam is roughly equivalent to a U.S. High School diploma. Rather confusingly, you can get As, Bs or Cs in your "A Level" results. Entrance to the better universities normally requires several As in your "A Levels".

The BIGGEST confusion in British terminology, however, surrounds use of the term "public school". Traditionally, a public school was where people who were rich but not rich enough to afford private tutors sent their kids. So a British public school is a fee-paying school. It is what Americans or Australians would call a private school. Brits are however aware of the confusion this causes benighted non-Brits so these days often in the media use "Independent" where once they would have used "public". The term for a taxpayer-supported school in Britain is a State school, but there are several varieties of those. The most common (and deplorable) type of State school is a "Comprehensive"

MORE TERMINOLOGY: Many of my posts mention the situation in Australia. Unlike the USA and Britain, there is virtually no local input into education in Australia. Education is mostly a State government responsibility, though the Feds have a lot of influence (via funding) at the university level. So it may be useful to know the usual abbreviations for the Australian States: QLD (Queensland), NSW (New South Wales), WA (Western Australia), VIC (Victoria), TAS (Tasmania), SA (South Australia).

There were two brothers from a famous family. One did very well at school while the other was a duffer. Which one went on the be acclaimed as the "Greatest Briton"? It was the duffer: Winston Churchill.

Another true modern parable: I have twin stepdaughters who are both attractive and exceptionally good-natured young women. I adore both of them. One got a university degree and the other was an abject failure at High School. One now works as a routine government clerk and is rather struggling financially. The other is extraordinarily highly paid and has an impressive property portfolio. Guess which one went to university? It was the former.

The above was written a couple of years ago and both women have moved on since then. The advantage to the "uneducated" one persists, however. She is living what many would see as a dream.

The current Left-inspired practice of going to great lengths to shield students from experience of failure and to tell students only good things about themselves is an appalling preparation for life. In adulthood, the vast majority of people are going to have to reconcile themselves to mundane jobs and no more than mediocrity in achievement. Illusions of themselves as "special" are going to be sorely disappointed

On June 6, 1944, a large number of young men charged ashore at Normandy beaches into a high probability of injury or death. Now, a large number of young people need safe spaces in case they might hear something that they don't like.

Perhaps it's some comfort that the idea of shielding kids from failure and having only "winners" is futile anyhow. When my son was about 3 years old he came bursting into the living room, threw himself down on the couch and burst into tears. When I asked what was wrong he said: "I can't always win!". The problem was that we had started him out on educational computer games where persistence only is needed to "win". But he had then started to play "real" computer games -- shootem-ups and the like. And you CAN lose in such games -- which he had just realized and become frustrated by. The upset lasted all of about 10 minutes, however and he has been happily playing computer games ever since. He also now has a First Class Honours degree in mathematics and is socially very pleasant. "Losing" certainly did not hurt him.

Even the famous Marxist theoretician Antonio Gramsci (and the world's most famous Sardine) was a deep opponent of "progressive" educational methods. He wrote: "The most paradoxical aspect is that this new type of school is advocated as being democratic, while in fact it is destined not merely to perpetuate social differences, but to crystallise them." He rightly saw that "progressive" methods were no help to the poor

"Secretary [of Education] Bennett makes, I think, an interesting analogy. He says that if you serve a child a rotten hamburger in America, Federal, State, and local agencies will investigate you, summon you, close you down, whatever. But if you provide a child with a rotten education, nothing happens, except that you're liable to be given more money to do it with." -- Ronald Reagan

I am an atheist of Protestant background who sent his son to Catholic schools. Why did I do that? Because I do not personally feel threatened by religion and I think Christianity is a generally good influence. I also felt that religion is a major part of life and that my son should therefore have a good introduction to it. He enjoyed his religion lessons but seems to have acquired minimal convictions from them.

Why have Leftist educators so relentlessly and so long opposed the teaching of phonics as the path to literacy when that opposition has been so enormously destructive of the education of so many? It is because of their addiction to simplistic explanations of everything (as in saying that Islamic hostility is caused by "poverty" -- even though Osama bin Laden is a billionaire!). And the relationship between letters and sounds in English is anything but simple compared to the beautifully simple but very unhelpful formula "look and learn".

For greatest efficiency, lowest cost and maximum choice, ALL schools should be privately owned and run -- with government-paid vouchers for the poor and minimal regulation.

"Now, what I want is Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else and root out everything else. You can only form the minds of reasoning animals upon Facts. Nothing else will ever be of service to them ... Stick to Facts, sir!" So spake Mr Gradgrind, Dickens's dismal schoolteacher in Hard Times, published 1854. Mr Gradgrind was undoubtedly too narrow but the opposite extreme -- no facts -- would seem equally bad and is much closer to us than Mr Gradgrind's ideal

The NEA and similar unions worldwide believe that children should be thoroughly indoctrinated with Green/Left, feminist/homosexual ideology but the "3 R's" are something that kids should just be allowed to "discover"

A a small quote from the past that helps explain the Leftist dominance of education: "When an opponent says: 'I will not come over to your side,' I calmly say, 'Your child belongs to us already. You will pass on. Your descendents, however, now stand in the new camp. In a short time, they will know nothing else but this new community.'." Quote from Adolf Hitler. In a speech on 6th November 1933

I am rather pleased to report that I am a lifelong conservative. Out of intellectual curiosity, I did in my youth join organizations from right across the political spectrum so I am certainly not closed-minded and am very familiar with the full spectrum of political thinking. Nonetheless, I did not have to undergo the lurch from Left to Right that so many people undergo. At age 13 I used my pocket-money to subscribe to the "Reader's Digest" -- the main conservative organ available in small town Australia of the 1950s. I have learned much since but am pleased and amused to note that history has since confirmed most of what I thought at that early age.

I imagine that the the RD is still sending mailouts to my 1950s address!

Discipline: With their love of simple generalizations, this will be Greek to Leftists but I see an important role for discipline in education DESPITE the fact that my father never laid a hand on me once in my entire life nor have I ever laid a hand on my son in his entire life. The plain fact is that people are DIFFERENT, not equal and some kids will not behave themselves in response to persuasion alone. In such cases, realism requires that they be MADE to behave by whatever means that works -- not necessarily for their own benefit but certainly for the benefit of others whose opportunities they disrupt and destroy.

Popper in "Against Big Words": "Every intellectual has a very special responsibility. He has the privilege and the opportunity of studying. In return, he owes it to his fellow men (or 'to society') to represent the results of his study as simply, clearly and modestly as he can. The worst thing that intellectuals can do - the cardinal sin - is to try to set themselves up as great prophets vis-à-vis their fellow men and to impress them with puzzling philosophies. Anyone who cannot speak simply and clearly should say nothing and continue to work until he can do so."

Many newspaper articles are reproduced in full on this blog despite copyright claims attached to them. I believe that such reproductions here are protected by the "fair use" provisions of copyright law. Fair use is a legal doctrine that recognises that the monopoly rights protected by copyright laws are not absolute. The doctrine holds that, when someone uses a creative work in way that does not hurt the market for the original work and advances a public purpose - such as education or scholarship - it might be considered "fair" and not infringing.

Comments above from Brisbane, Australia by John J. Ray (M.A.; Ph.D.) -- former teacher at both High School and university level

There are also two blogspot blogs which record what I think are my main recent articles here and here. Similar content can be more conveniently accessed via my subject-indexed list of short articles here or here (I rarely write long articles these days)

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